A reader of Mike Norman's very useful blog calls my last post a vacuous response to Ramanan. Of course it was not a response at all, merely a commentary. Notice how I said that "all the criticisms can be defended in two words: endogenous money!", not that they were defended... Plus I thought it implicit that whenever one says something like "I got n words for you: word_1 ... word_n", one's tongue is firmly in one's cheek. But I'm quickly learning that there is no such thing in the econo-blogosphere.

In any event, after the avalanche of comments on Mike's re-posts (last count: 21 on the post above, 66 on Ramanan's second take down, and 124 on its predecessor), perhaps it's time for a point-by-point reply (I originally called it a "point-by-pint" reply, which is perhaps a measure of what was on my mind while I was writing it).

Let me start by saying that I'll refer mostly to this paper, since I had something to do with the notation and ideas presented in it, rather than to Steve's presentation at the UMKC conference, thought I might occasionally refer to it too. Let me also say that said paper (which is being refereed and therefore can sill improve quite a lot), could use a great deal of clarifications. Many of the ideas that were in the back of our minds as we were writing it clearly didn't make it to the printed page, so I welcome the opportunity to elaborate.

With these in mind, here are the essential points:

(1) Our "closed" economy does consist of firms, households, and banks, but we find it useful to

**separate the banking sector from the rest of the private sector**. We do this explicitly on pages 18 to 23, but leave it implicit on page 15, which contains the passages that Ramanan has a beef with. So our "change in debt" is really change in debt of the non-bank private sector to the banking sector, which obviously does not need to cancel out in the aggregate (i.e excluding banks). This is in contrast with the view that "one person's asset is another person's liability", which underlines the view that firm's debt is mirrored by household's savings.

(2)

**Debt only matter after it has been spent**. This is the point of equation (1.5): we assume that investment is financed by retained earnings plus change in debt. If new debt is not spent, it doesn't finance anything, so we don't count it in the model.

(3)

**Accounting rules!**The whole point of the Appendix in the paper is to show that recorded income equals recorded expenditure at the end of a given period (say one year). We don't use continuous mathematics to upset accounting identities, but rather as "a simple way to represent the conceptual difference between spending plans and current received income".

Observe that all 3 points are intimately connected with the idea of endogenous money, which is what I meant by my "two words" zinger. The effects of endogenous money only become apparent when banks are disaggregated from the rest of the private sector (1), capitalists finance new investment above and beyond savings by creating deposits through endogenous money (2), and spending plans exceed current received income for the same reason, even if this is not apparent when one measures recorded income and recorded expenditure (3).

In the end, what we are tying to capture is the idea expressed on page 10, namely that "the essence of endogenous money hypothesis is that banks create spending power for borrowers without reducing the spending power of savers."

Judging by the criticism, we haven't quite succeeded yet, but we'll keep on trying.

I cannot understand Ramanan's critique as it was very unclear, but his basic point was right - your accounting doesn't work, as far as I can tell.

ReplyDeleteLook up the Kalecki profit equation (or the Levy profit equation; there's a good summary in a paper at the Levy Institute). The full equation is pretty complicated, but for the simplified economy you have (aggregated private sector, no external sector or government, or household saving), the equation reduces to (or so I hope...):

Undistributed profits = business sector investment.

I.e., business investment is self-financing under these conditions. There is no need for debt financing in your equation.

Why you may need debt financing in a model is that you have a business sector split into a consumer goods and a capital goods sector. The consumer good sector needs to borrow to invest, but that becomes a source of profits (and cash) for the capital goods sector. Thus the investment is done by one sub-sector, and the profits appear in another sub-sector.

Since your model has aggregated the business sector into a single entity, the increase in debt in the business sector will coincide with an increase in bank deposits for the same sector. You have superimposed a non-necessary behavioral condition that debt growth matches investment - the investment could have been financed by the business sector's increasing bank balances. Your equations, as far as I can decipher them, are missing the profit flow created by the investment.

I would recommend reading (or re-reading) the Godley & Lavoie book, and the part about the business capital account.

Aside on continuous time: using continuous time is a particular nightmare in your modelling. You have to implicitly include a lot of continuity conditions on your time series in order to be able to move from the accounting identities that define economic systems to point-in-time conditions.

Bond Guy,

DeleteWanted to ask which parts I was not clear - for a feedback.

This is because I am in complete agreement with you. (And other people in agreement with me found it generally clear).

Also, see my comment(s) in the previous post where I show that either one assumes workers have to save or else Π_R = I.

"Aside on continuous time: using continuous time is a particular nightmare in your modelling. You have to implicitly include a lot of continuity conditions on your time series in order to be able to move from the accounting identities that define economic systems to point-in-time conditions."

Very good point. This is the reason I suggested the usage of the Dirac delta function.

Not that I would like to use it myself . Just for others who want to make a connection.

(One cannot assume debt injections as discontinuous and at the same time income flows as continuous).

Further explanation. You wrote quite a bit, and yes you correctly (in my view) argued that the accounting is wrong. But within your text, I'm not sure I see the exact reason why the equation you pinpointed was wrong. But if the accounting identity used is the Kalecki profit equation, the contradiction is obvious.

DeleteMore specifically, let

e(t) = (undistributed profit in the business sector)(t) - investment(t) [for the simplified economy].

According to the Keen equation, e(t) equals the change in debt.

However, the accounting identity requires that (Latex notation, \int = integral)

\int_{t^0}^{t_f} e(t) = 0, \forall t_0, t_f.

If we make strong continuity assumptions (continuous function except at a finite number of points, for example), it is a basic exercise to verify that e(t) = 0 \forall t. [If we don't make such continuity assumptions, e(t) can be arbitrary values over sets of zero measure (E.g., over all rational numbers.)]

Thus, we cannot have the change in debt term in there.

However, one way it could be preserved is to assume that the banking sector is the sector selling the capital goods (it gets the profits from the sale of capital goods, and the increase in bank loans is matched by an increase in bank equity, not an increase in deposits. That's a fairly unusual model, to say the least.

Bond Guy,

DeleteI said workers' saving and investment are zero in the model. So one just needs to consider capitalists saving and investment.

Capitalists' Saving is Pi_R

Capitalists' Investment is I

Since Saving = Investment for an economy as a whole (closed),

these difference between the two should be equal to zero and the difference between the two can only be equal to ΔD if ΔD is zero.

Are you saying that investment requires savings or investment causes saving?

DeleteIf I get a $100 loan from the bank and spend it on capital goods my spending has created savings but it didn't require them.

Has not the increase in debt temporarily added to demand?

And when it's paid back will it not then decrease demand by an equal amount?

This seems to imply that, although the overall effect of credit creation on AD is indeed equal to zero, that, depending on what point in the life cycle of the loan from views it from, the effect on AD can be either positive or negative.

The seemingly contradictory statements

- the change in debt does not affect AD

- the change in debt does affect AD

turn out to be perfectly reconcilable and equally true.

Is any of this an even remotely close to an accurate description of Mr. Grasselli's views?

"The whole point of the Appendix in the paper is to show that recorded income equals recorded expenditure at the end of a given period (say one year). We don't use continuous mathematics to upset accounting identities, but rather as "a simple way to represent the conceptual difference between spending plans and current received income".

ReplyDeleteSorry to be bugging ... But assuming the proof is correct.

If you model debt injections as step functions, you should use delta functions for income/expenditure flows.

Your models will be better off if you have two sets of variables Y_E, Y_I and Y_E(e) and Y_I(e).

Y_E = Y_I (*always and always*)

whatever Y_E(e) is doing.

By using the same variable for two different things will lead you to future paths which are not possible in real life.